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View Poll Results: What price point would you thake the deal?
I would take it for $900 (please also tick all boxes below except box 6) 6 6.38%
I would take it for $600 (please also tick all boxes below except box 6) 17 18.09%
I would take it for $250 (please also tick all boxes below except box 6) 33 35.11%
I would take it for $100 (please also tick all boxes below except box 6) 37 39.36%
I would take it for $50 44 46.81%
I would not take this deal, even for $50 50 53.19%
Multiple Choice Poll. Voters: 94. You may not vote on this poll

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  #1  
Old 07-26-2017, 10:09 AM
Mr Shine Mr Shine is offline
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Pick a card, any card and win $50,000.

I pick up a genuine new pack of cards, remove the jokers and black aces, fully shuffle it and allow you to cut the cards. You know I have no slight of hand skills, you examined the deck already and you got to choose where to cut. In other words assume for the hypothetical there is no funny business.

I then offer you a wager, if you can tell me the topmost card i will give you $US 50,000. The amount I'm offering is not up for negotiation.

On a strict EV the real value of money this opportunity is worth $1000 exactly, but nobody would pay that. At what price point would you take the offer?

Last edited by Asimovian; 07-26-2017 at 10:22 AM.. Reason: Removed typo at OP's request.
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  #2  
Old 07-26-2017, 10:11 AM
Johnny Bravo Johnny Bravo is online now
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I'd buy that for a dollar.
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  #3  
Old 07-26-2017, 10:27 AM
TriPolar TriPolar is offline
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Well I said I wouldn't do it for $50, but I was considering I only had one shot at it. If I could play repeatedly I might spend some money. But assuming the cards are reshuffled each time there's no guarantee I'll ever win, so I'm still inclined not to spend even $10 on a single chance. A buck or two? Sure, I'll give it a go
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  #4  
Old 07-26-2017, 10:30 AM
Little Nemo Little Nemo is online now
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I'd do it for ten dollars. I might go as high as twenty depending on my mood at the moment. But fifty's too high.

I realize this is not mathematically logical but there you go.
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  #5  
Old 07-26-2017, 10:51 AM
Jophiel Jophiel is online now
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Ace of Spades!

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Originally Posted by Mr Shine View Post
I pick up a genuine new pack of cards, remove the jokers and black aces...
D'oh!
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  #6  
Old 07-26-2017, 11:26 AM
Shodan Shodan is online now
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As a one-off, no thanks. The more I can repeat, the higher I will go.

Regards,
Shodan
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  #7  
Old 07-26-2017, 11:33 AM
JohnGalt JohnGalt is online now
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Not going to take the bet. As Sky Masterson says in Guys and Dolls

Quote:
One of these days in your travels, a guy is going to show you a brand-new deck of cards on which the seal is not yet broken. Then this guy is going to offer to bet you that he can make the jack of spades jump out of this brand-new deck of cards and squirt cider in your ear. But, son, do not accept this bet, because as sure as you stand there, you're going to wind up with an ear full of cider.
I don't want an ear full of cider; there's always funny business....
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  #8  
Old 07-26-2017, 11:46 AM
Chronos Chronos is online now
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Likewise. Even if you don't have any sleight of hand skills (and how do I know this, again?), there are a thousand other ways you could have rigged the game. And you wouldn't even be offering the game at all if you hadn't rigged it in some way.
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  #9  
Old 07-26-2017, 12:00 PM
Horatius Horatius is online now
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Going with the "Assume there's no funny business" is real, then mathematically you should take the $900 bet, as the expected value is greater than that. However, I only opted for the $600 and less versions on the standing theory that I never bet more than I'm willing to lose. That break point is obviously somewhere between 600 and 900.
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  #10  
Old 07-26-2017, 12:53 PM
iamthewalrus(:3= iamthewalrus(:3= is online now
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Originally Posted by Horatius View Post
Going with the "Assume there's no funny business" is real, then mathematically you should take the $900 bet, as the expected value is greater than that. However, I only opted for the $600 and less versions on the standing theory that I never bet more than I'm willing to lose. That break point is obviously somewhere between 600 and 900.
EV is not the only consideration in whether or not you should take a bet.

What you want here is The Kelly Criterion, which tells you how much you should wager on a bet based both on its odds and on the size of your bankroll.

As the size of the bet goes up compared to your bankroll, the odds you need to take it go up too.

Note that if you cut the price and payout both by a factor of 1000, most people would be more willing to pay $0.90, because it's a smaller portion of their "bankroll".

I also said $600. I can afford to lose that, and the EV at $600 is very good.
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  #11  
Old 07-26-2017, 12:55 PM
iamthewalrus(:3= iamthewalrus(:3= is online now
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Originally Posted by Shodan View Post
As a one-off, no thanks. The more I can repeat, the higher I will go.

Regards,
Shodan
Isn't this just textbook Gambler's fallacy? If a bet is worth making multiple times, it's worth making once.
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  #12  
Old 07-26-2017, 01:05 PM
pulykamell pulykamell is online now
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Originally Posted by Chronos View Post
Likewise. Even if you don't have any sleight of hand skills (and how do I know this, again?), there are a thousand other ways you could have rigged the game. And you wouldn't even be offering the game at all if you hadn't rigged it in some way.
Oh, let's not fight the hypothetical here. Let's take the game as fair and Mr Shine at his word. That's the whole point of this question. With the "pot odds" so much in your favor, what amount would you be willing to risk?

I was waffling between $250 and $100, and I just went with $100. I could live with myself losing $100 98% of the time for a 2% chance of winning $50K. Losing a hundred bucks isn't going to change my life in any meaningful way. Winning $50K will help with a good number of things. I should probably up it to $250, but I don't feel like I could shake off a $250 loss as easily as a $100 loss. No idea why, but that's just my feeling. No logic to it, given I'm getting 4x pot odds (or however that number is properly expressed.)
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  #13  
Old 07-26-2017, 01:14 PM
Jack Batty Jack Batty is offline
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I think I'm confused. Why would I lay $900 up against $50,000 when I could only lay $50. Can I just guess for free and you give the 50 grand if I'm right?

Last edited by Jack Batty; 07-26-2017 at 01:14 PM..
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  #14  
Old 07-26-2017, 01:15 PM
Dead Cat Dead Cat is offline
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I believe the largest amount I have wagered on a single roulette spin/hand of Blackjack is $200 (200 actually, but these days it's not much different!). The pay-off there is slightly worse than 50%. Therefore logically, I should be jumping at the chance to do this for $100, or probably even $250. But in reality, the odds of success are low, and therefore I am not willing to risk this much. I guess this is just me applying my own vague notion of the Kelly Criterion. I voted $50.
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  #15  
Old 07-26-2017, 01:17 PM
Lemur866 Lemur866 is online now
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Quote:
Originally Posted by iamthewalrus(:3= View Post
EV is not the only consideration in whether or not you should take a bet.

What you want here is The Kelly Criterion, which tells you how much you should wager on a bet based both on its odds and on the size of your bankroll.

As the size of the bet goes up compared to your bankroll, the odds you need to take it go up too.

Note that if you cut the price and payout both by a factor of 1000, most people would be more willing to pay $0.90, because it's a smaller portion of their "bankroll".

I also said $600. I can afford to lose that, and the EV at $600 is very good.
Exactly right. People will pay a dollar for a 1 in 50 chance to win $50. Heck, they regularly pay more than a dollar for that. But a thousand dollars for the chance to win $50,000 is different. And that's because they reason that they won't feel the loss of $1 but they'd feel the gain of $50. However, they'd feel the loss of $1000, so it's a much worse bet for them. In fact people regularly pay for insurance where they pay a small amount to avoid the risk of losing a large amount.
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  #16  
Old 07-26-2017, 01:20 PM
Mr Shine Mr Shine is offline
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Quote:
Originally Posted by Jack Batty View Post
I think I'm confused. Why would I lay $900 up against $50,000 when I could only lay $50. Can I just guess for free and you give the 50 grand if I'm right?
I'm asking which ones you'd take. The question would you take $900? assumes that's as low as I'm willing to go. (If the answer to that is "yes", it naturally follows that you would also take 600, 250, 100 or 50 unless you have some weird reasoning I'd like to hear about)
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  #17  
Old 07-26-2017, 01:35 PM
Jack Batty Jack Batty is offline
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Sorry. I'm still not getting it. I'm either a little thick or I'm not grocking your terminology.

Here's the way I'm reading it - if I can guess the top card in a shuffled deck, you will give me $50,000 dollars, but I have to make a bet to earn it. Do I want to bet $50 bucks for the chance to win $50,000 or do I want to bet $900 to win $50,000. I'll take the $50 bet every time. Why would I risk more for the same payout?

Or is that where my misunderstanding lies?
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  #18  
Old 07-26-2017, 01:45 PM
Rysto Rysto is online now
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Quote:
Originally Posted by Jack Batty View Post
I'll take the $50 bet every time. Why would I risk more for the same payout?

Or is that where my misunderstanding lies?
Think of it like an auction. How high are you will to go in order to make the bet? Note that you're supposed to select all of the bets you're willing to make, so if you select $900 then select all of the lower amounts too.
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  #19  
Old 07-26-2017, 01:50 PM
Jack Batty Jack Batty is offline
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Again, maybe it's me. Why would I risk losing $900 for the chance for $50,000 when I can risk losing only $50 for the same $50,000?

I'm kind of feeling like an idiot here. I think there's something I'm not reading right.
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  #20  
Old 07-26-2017, 01:52 PM
Lemur866 Lemur866 is online now
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He's not asking what your minimum bet would be. He's asking your maximum bet.

If he offered you the bet for $1000 would you accept? How about $900? How about $800? How about $100?

What is the largest number you'd agree to bet?

Imagine there are 100 tables, each with 100 Professor Shines. The first table offers the bet for $10. The second for $20, the tenth for $100 and the 100th for $1000.

You walk along the tables. You think to yourself that you'd play the first game, and the second game, and the third game, and the tenth game. How far down the tables would you go before you think to yourself that you wouldn't play that game?
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  #21  
Old 07-26-2017, 01:53 PM
Jack Batty Jack Batty is offline
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Oooh. Okay. I think something just rattled loose in my noggin. Even if I'm only willing to risk the $50, there's no guarantee he'll take the bet. I was reading it as the bet is on regardless of how much I was willing to bet.
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  #22  
Old 07-26-2017, 02:12 PM
Telemark Telemark is online now
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Quote:
Originally Posted by Jack Batty View Post
Here's the way I'm reading it - if I can guess the top card in a shuffled deck, you will give me $50,000 dollars, but I have to make a bet to earn it. Do I want to bet $50 bucks for the chance to win $50,000 or do I want to bet $900 to win $50,000. I'll take the $50 bet every time. Why would I risk more for the same payout?
A mathematical calculation of the odds suggests that the bet is worth $1000; you have a 1/50 chance to win $50,000. But most folks wouldn't put that much of their own money on the line even though the math says they should. It's too big a risk, they can't afford to lose $1000, they're risk averse, etc.

The question here is how much would he need to lower the price of the bet before you felt comfortable putting up your own money and taking the wager. This says nothing about whether the dealer will accept your offer, just how much are you willing to spend for the chance.
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  #23  
Old 07-26-2017, 02:18 PM
Surreal Surreal is offline
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Originally Posted by iamthewalrus(:3= View Post
If a bet is worth making multiple times, it's worth making once.
Wrong. The more times you play, the less of a role random chance will play in your results and the more likely your results will approach the mathematical expected value.
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  #24  
Old 07-26-2017, 02:21 PM
Jack Batty Jack Batty is offline
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Well, I probably still wouldn't go $50 so I don't think I'd be in the running anyway. I'm not much of a lottery player. I don't mind throwing some money away on chance but only as much as I'm willing to throw away. Maybe a buck or two. I believe I've gone as high as shelling out five dollars to get in on the sweet, sweet Power Ball multiplier action that I would never see either.
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  #25  
Old 07-26-2017, 03:53 PM
Lemur866 Lemur866 is online now
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It's funny. That 1 in 50 chance is so small that people treat it as essentially impossible, and so any bet even at $50 is too much.

But if you offered them $2000 on a coin flip and then asked how much they'd bet, you'd probably get a lot higher numbers, even though the expected value is exactly the same: $1000.
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  #26  
Old 07-26-2017, 04:10 PM
Jack Batty Jack Batty is offline
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I've been thinking about it. It seems to me it's more about one's stack than what kind of odds one might get. I mean, like I said, I'm willing to pony a dollar for a chance to win that $50,000. But I'd also be willing to bet that same dollar for the same chance to win $50. I wouldn't bet that dollar for a one in fifty chance to win twenty-five dollars, nor would I bet five dollars to win that $50. Like I said, I consider a wager like that is most likely thrown away anyhow, so once the odds tip against the payout, I'm gone. But I'm only ever in for a buck.

I'd put a buck down on a coin flip for a buck, if I were in the mood. Same for the $2,000.
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  #27  
Old 07-26-2017, 06:28 PM
iamthewalrus(:3= iamthewalrus(:3= is online now
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Originally Posted by Surreal View Post
Wrong. The more times you play, the less of a role random chance will play in your results and the more likely your results will approach the mathematical expected value.
Only if you have an unlimited bankroll.

In real life, bets are a random walk that sometimes hits 0 and then you're done.

Think of it this way: You're not willing to make one bet because the variance is too high. But the variance of each bet isn't changed. And you still have to make the decision to make the next bet each time.

After you make that first $900 bet and lose, are you then going to feel better about making the second bet, now that you're $900 closer to bankrupt, and your odds haven't changed? Kelly says you should be less willing to make the bet the second time (regardless of how many more times you are allowed to make the bet).
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  #28  
Old 07-26-2017, 08:51 PM
Pantastic Pantastic is online now
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Originally Posted by Lemur866 View Post
It's funny. That 1 in 50 chance is so small that people treat it as essentially impossible, and so any bet even at $50 is too much.

But if you offered them $2000 on a coin flip and then asked how much they'd bet, you'd probably get a lot higher numbers, even though the expected value is exactly the same: $1000.
That's because EV is not the only number relevant to analyzing whether a bet is a good bet or not. The fact that 49 times out of 50 you're simply out of your money, and that you need a bankroll in the tens of thousands to stand a decent chance of breaking even is relevant too.
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  #29  
Old 07-26-2017, 08:55 PM
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I voted that I just wouldn't take the bet. It's not a type of gambling that interests me, the chance of winning something is too low, and $50 or more is enough to count as 'real money' for me. (I'd be willing to play if I was paying $1 for the chance to win $60, because the $1 isn't enough to hurt if I lose). If I want to gamble with a significant amount of money, I'd much rather play poker than a card picking game. And in practice, as opposed to hypothetical, I'd expect this to be a scam anyway.
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  #30  
Old 07-27-2017, 01:24 AM
Mr Shine Mr Shine is offline
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OK those who wouldn't pay $50 for the opportunity does it change if it's "found money"? Say you're in the studio audience of Oprah Winfrey's show, you get randomly picked and she offers you either a crisp $50 bill or a 1/50 chance at 50K?
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  #31  
Old 07-27-2017, 01:32 AM
Mr Shine Mr Shine is offline
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Also

I would take it for $50 17 45.95%
I would not take this deal, even for $50 19 51.35%
Multiple Choice Poll. Voters: 37.

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  #32  
Old 07-27-2017, 01:35 AM
Mr Shine Mr Shine is offline
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Originally Posted by Pantastic View Post
That's because EV is not the only number relevant to analyzing whether a bet is a good bet or not. The fact that 49 times out of 50 you're simply out of your money, and that you need a bankroll in the tens of thousands to stand a decent chance of breaking even is relevant too.
Note you don't have a bankroll. You have one go, and you're done.
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  #33  
Old 07-27-2017, 02:16 AM
Little Nemo Little Nemo is online now
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Originally Posted by Mr Shine View Post
OK those who wouldn't pay $50 for the opportunity does it change if it's "found money"? Say you're in the studio audience of Oprah Winfrey's show, you get randomly picked and she offers you either a crisp $50 bill or a 1/50 chance at 50K?
Then I would go for the chance of the fifty thousand.
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  #34  
Old 07-27-2017, 08:01 AM
Mangetout Mangetout is offline
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Originally Posted by pulykamell View Post
Oh, let's not fight the hypothetical here. Let's take the game as fair and Mr Shine at his word. That's the whole point of this question. With the "pot odds" so much in your favor, what amount would you be willing to risk?
Trouble is, it's a poll asking 'what would you be prepared to accept?" I don't think it's very easy to split out reluctance driven by perception of odds from reluctance driven by perception of scam.
I get that the hypothetical is an honest deal, but that's only half the equation - my gut and heart is the other.

I don't have an answer.
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  #35  
Old 07-27-2017, 08:47 AM
ftg ftg is offline
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The problem in the OP carried further is the famous St. Petersburg Paradox.

The expected value of winnings seems to have little to do with people's actual comfort in betting.
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  #36  
Old 07-27-2017, 08:47 AM
pulykamell pulykamell is online now
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Originally Posted by Mangetout View Post
I don't think it's very easy to split out reluctance driven by perception of odds from reluctance driven by perception of scam.
For me, it's no problem. It's just a hypothetical, so it's pretty easy to filter out the scam part of the equation. If I thought at all it was a scam, I wouldn't take the bet at all, of course. But in the world of the hypothetical where everything is as it seems, my answer is somewhere around $100-$250.

This isn't a real-world question, but I'm sure one can come up with a real world example that is completely legit on the face of it with the same odds and the same question. Like, I duuno, for a tortured example, let's say a church is having a lottery for $50,000 that's been a rolling jackpot that's built up over time that no one has won. At the end of the year, they need to finally award the prize so they can close out their accounts for the year or whatever. They will sell 50 tickets. One of those will be chosen and the winner will receive $50,000. You can only buy one ticket. What's the maximum price you would pay for it? Or, if the church were selling the tickets for $50 a piece, would you buy one? If they were $100 a piece, would you buy one? If they were $250 a piece, would you buy one? Etc.

Last edited by pulykamell; 07-27-2017 at 08:49 AM..
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  #37  
Old 07-27-2017, 09:38 AM
Pantastic Pantastic is online now
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Originally Posted by Mr Shine View Post
Note you don't have a bankroll. You have one go, and you're done.
That's not something to note, that's a new restriction in the hypothetical that you didn't include in the text originally. Doesn't significantly change my answer,instead of requiring a large bankroll, it's just flat-out impossible to make the bet enough times for me to consider EV a very relevant statistic.
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  #38  
Old 07-27-2017, 09:49 AM
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Originally Posted by ftg View Post
The problem in the OP carried further is the famous St. Petersburg Paradox.

The expected value of winnings seems to have little to do with people's actual comfort in betting.
Well, in the St Petersburg Paradox the calculated EV requires the house (whoever is running the game) to stay in business forever and to have an infinite bankroll. Since neither of those conditions actually hold in the real world, it would be rather silly to take the calculated EV seriously. And as the Wiki article points out, even if the house had infinite money and infinite coin flips, there would be no reason to offer the game because they would expect to lose eventually.

It's really a pretty degenerate case for EV, it surprises me that it gets so much attention. The EV is a contrived mathematical number that really doesn't work well in this case, and people's intuition is built around real situations while the paradox is built around a situation that requires several impossibilities and a person/organization acting on purely self-destructive motives.
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  #39  
Old 07-27-2017, 12:00 PM
Doctor Jackson Doctor Jackson is online now
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EV is pretty useless on one time events. Consider a lottery with 10 million number combinations and only offers a grand prize. Math says that when the jackpot is $10 million, the EV is 1. That does not mean I can expect to receive $1 for my $1 bet on any given occurrence. It means I have a .0000001% chance of winning a huge amount and a 99.9999999% chance of losing my dollar.
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  #40  
Old 07-27-2017, 12:25 PM
Horatius Horatius is online now
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Quote:
Originally Posted by Doctor Jackson View Post
EV is pretty useless on one time events. Consider a lottery with 10 million number combinations and only offers a grand prize. Math says that when the jackpot is $10 million, the EV is 1. That does not mean I can expect to receive $1 for my $1 bet on any given occurrence. It means I have a .0000001% chance of winning a huge amount and a 99.9999999% chance of losing my dollar.


But EV does help you in determining how honest the game is, by how great a difference there is between the EV and the bet.

Using your example, with an EV of 1 or more, there's essentially no way the lottery can make money over time, so if they're offering that, it's reasonable to conclude there is a scam of some sort going on, limitations of the OP notwithstanding.

For the lottery to make sense, the EV has to be less than 1, so that the house has a built in edge. Then it becomes a question of how much edge? If the EV is only 0.5, that's pretty bad. Not actually a scam, but any serious gambler knows there's lots of games with better odds out there, and would go play those instead.

That's the OP's biggest problem - even at the $900 bet level, if 50 people accepted the deal, he'd bring in $45,000, but likely pay out the $50,000.
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  #41  
Old 07-27-2017, 01:58 PM
Mr Shine Mr Shine is offline
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Originally Posted by Doctor Jackson View Post
EV is pretty useless on one time events. Consider a lottery with 10 million number combinations and only offers a grand prize. Math says that when the jackpot is $10 million, the EV is 1. That does not mean I can expect to receive $1 for my $1 bet on any given occurrence. It means I have a .0000001% chance of winning a huge amount and a 99.9999999% chance of losing my dollar.
EV is certainly useful in one time events. The problem with huge sums like $10 million (and to a lesser extent $50000) is that the utility of money decreases at high amounts, (winning $1 million would make me ecstatic, winning $10 million won't make me much more happier), so you have to factor that in, but looking at the EV is a good start.

Last edited by Mr Shine; 07-27-2017 at 02:01 PM..
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  #42  
Old 07-27-2017, 02:17 PM
iamthewalrus(:3= iamthewalrus(:3= is online now
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Originally Posted by Horatius View Post
Using your example, with an EV of 1 or more, there's essentially no way the lottery can make money over time, so if they're offering that, it's reasonable to conclude there is a scam of some sort going on, limitations of the OP notwithstanding.
If someone were literally offering this game as stated, yes, it's a loser for the house.

But focusing on that and assuming that it's a "scam" is both fighting the hypothetical and missing the point.

The interesting part of this question is how people deal with risk. And it is interesting in its own light. There are quite a few who apparently are incredibly risk averse. Fully half of respondents are unwilling to bet $50 to win an expected $1000. That implies (to me) some combination of extreme poverty, innumeracy, or unreasonable risk-averseness. Which is interesting.

And the fact is there are tons of real-life examples of risky bets that have positive expected values. Because life is not a zero sum game. Starting a business, for example, has pretty long odds, but a huge payoff.

Last edited by iamthewalrus(:3=; 07-27-2017 at 02:18 PM..
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  #43  
Old 07-27-2017, 03:03 PM
Mangetout Mangetout is offline
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Originally Posted by pulykamell View Post
For me, it's no problem. It's just a hypothetical, so it's pretty easy to filter out the scam part of the equation. If I thought at all it was a scam, I wouldn't take the bet at all, of course. But in the world of the hypothetical where everything is as it seems, my answer is somewhere around $100-$250.

This isn't a real-world question, but I'm sure one can come up with a real world example that is completely legit on the face of it with the same odds and the same question. Like, I duuno, for a tortured example, let's say a church is having a lottery for $50,000 that's been a rolling jackpot that's built up over time that no one has won. At the end of the year, they need to finally award the prize so they can close out their accounts for the year or whatever. They will sell 50 tickets. One of those will be chosen and the winner will receive $50,000. You can only buy one ticket. What's the maximum price you would pay for it? Or, if the church were selling the tickets for $50 a piece, would you buy one? If they were $100 a piece, would you buy one? If they were $250 a piece, would you buy one? Etc.
I find it harder to filter out my feelings on the matter from my logic - I wonder if that comes from not really being an experienced gambler at all.
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Old 07-27-2017, 03:29 PM
Pantastic Pantastic is online now
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Originally Posted by iamthewalrus(:3= View Post
But focusing on that and assuming that it's a "scam" is both fighting the hypothetical and missing the point.

The interesting part of this question is how people deal with risk.
The risk of something being a scam is a huge part of evaluating real world risk, it's not something you can just casually dismiss. That's why it's silly to do like some graduate students and look at a study that has someone standing on a corner handing out cash, note that a large portion of people turn down the cash, and conclude that people don't like unearned money. What's really going on is that a person on a street corner offering to hand you cash is FAR more likely to be a scam artist sucking you into a scheme than someone who's really handing out money with no strings attached.

Quote:
And it is interesting in its own light. There are quite a few who apparently are incredibly risk averse. Fully half of respondents are unwilling to bet $50 to win an expected $1000. That implies (to me) some combination of extreme poverty, innumeracy, or unreasonable risk-averseness. Which is interesting.
But in ordinary English language, you don't expect to win $1000, you expect to lose $50. You're conflating the specific mathematical term "Expected value" with something being a reasonable expectation in plain English. It's certainly not reasonable to expect $1000 in this case, since you'll never actually win $1000 - most of the time you get nothing, rarely you get $50k.
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Old 07-27-2017, 05:01 PM
iamthewalrus(:3= iamthewalrus(:3= is online now
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Originally Posted by Pantastic View Post
The risk of something being a scam is a huge part of evaluating real world risk, it's not something you can just casually dismiss.
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Originally Posted by OP
In other words assume for the hypothetical there is no funny business.
He even put it in bold. I'm not saying scams don't exist. I'm saying that the OP clearly intended to discuss risk tolerance, not ability to sniff out a scam.

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You're conflating the specific mathematical term "Expected value" with something being a reasonable expectation in plain English.
I'm not. I'm using the mathematical term. My analysis of the results doesn't rely on a misunderstanding of English.

Yes, 98% of the time you're going to lose your $50. But being unwilling to wager $50 for the 2% chance of $50k suggests one or more of extreme poverty, extreme risk-averseness, or innumeracy. Or, I guess, unwillingness to consider the hypothetical as stated.

That's simply a wacky decision. 2% is small, but it's not "winning the lottery" small. If you're counting a 2% chance the same as a 0.0000001% chance, you do not understand how numbers work.
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Old 07-27-2017, 05:30 PM
Lemur866 Lemur866 is online now
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Or, let's take the inverse of this game. You pick the card. If it's anything but the Queen of Spades, you get paid $1000 + $X. If it's the Queen of Spades, you pay $50,000.

How large does X need to be before you agree to play this game?

It seems like for a lot of people the amount of X won't figure into it. Either you're willing to take a small change of ruin to win a small amount, or you're not. And it turns out that investors are regularly willing to make these sorts of bets: http://www.investopedia.com/terms/b/blackswan.asp
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Old 07-27-2017, 06:19 PM
Saltire Saltire is offline
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Basically, I'm not in a situation where I can feel good about losing $50 or more. So I can't feel good about playing that game, unless I happen to win, which is quite unlikely.

But I would probably play with someone else's money, like in the Oprah variation.
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Old 07-27-2017, 06:38 PM
Pantastic Pantastic is online now
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Originally Posted by iamthewalrus(:3= View Post
I'm not. I'm using the mathematical term. My analysis of the results doesn't rely on a misunderstanding of English.
Then if you're using the mathematical term, stick to the actual term and don't muddy the waters by using an English phrase that is similar but doesn't mean the same thing. You specifically said "Fully half of respondents are unwilling to bet $50 to win an expected $1000" - but there is no expected $1000. Literally no one will ever win $1000 in the game as stated, most people will win $0, some will win $1000. The EV is $1000, but that doesn't mean there is "an expected $1000" anywhere in the scenario. And because it's been made explicit that you only can play the game one time, there's no way to do multiple trials, which is the way to make any sort of average a sensible measure.

Quote:
Yes, 98% of the time you're going to lose your $50. But being unwilling to wager $50 for the 2% chance of $50k suggests one or more of extreme poverty, extreme risk-averseness, or innumeracy. Or, I guess, unwillingness to consider the hypothetical as stated.
Or maybe people evaluate a decision that throws away a 'week affecting' amount of money 98% of the time but wins 'nice but not life altering money' 2% of the time differently than you do. EV calculations are of mathematical interest, but are rahter often of no practical interest, and people like you that hold EV as some absolutely sacred thing that can never be questioned while insulting and dismissing people who consider other factors are not nearly as smart as you think you are.

Last edited by Pantastic; 07-27-2017 at 06:38 PM..
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Old 07-27-2017, 06:57 PM
Chronos Chronos is online now
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We can't assume that there's no funny business, because the OP tells us that there is funny business. Someone offering me a positive-EV bet on the pick-a-card game is, in itself, funny business. Saying that there is no funny business is, right from the start, fighting the hypothetical.
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Old 07-27-2017, 09:04 PM
UltraVires UltraVires is online now
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Originally Posted by Pantastic View Post
But in ordinary English language, you don't expect to win $1000, you expect to lose $50. You're conflating the specific mathematical term "Expected value" with something being a reasonable expectation in plain English. It's certainly not reasonable to expect $1000 in this case, since you'll never actually win $1000 - most of the time you get nothing, rarely you get $50k.
I agree with this. It would be great if I won $50k, but there is only 1/50 chance of that. There is a 49/50 chance that I will lose $50, which was my dinner or drink money that evening, and that would suck.

Which is the opposite of:

Quote:
Originally Posted by Lemur866
Or, let's take the inverse of this game. You pick the card. If it's anything but the Queen of Spades, you get paid $1000 + $X. If it's the Queen of Spades, you pay $50,000.

How large does X need to be before you agree to play this game?
I might play for $0. A full 49 out of 50 times, I walk away with a grand in my pocket. Only 1 time out of 50 would disaster strike.

It may be a mental thing, but I tend to agree that people are misapplying the term "expected" value. In the OPs scenario, I don't expect $1k. I expect almost certainly losing my bet with an outside chance of hitting it big. There is a huge difference between the two.
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